Hello, I am completely lost with this problem. Any guidance is greatly appreciated.

Let $\displaystyle \Omega=\{(x,y):0<x\leq 1,0<y\leq 1\}$, let $\displaystyle \mathcal{B}^2$ be the $\displaystyle \sigma$-field of Borel subsets of $\displaystyle \Omega$ and let $\displaystyle P=\lambda_2$ be the Lebesgue measure on $\displaystyle \mathcal{B}^2$. Let $\displaystyle A_0=\{(x,y):x>0,y>0,x+y\leq 1\}$.

a. Starting from the fact that $\displaystyle \mathcal{B}^2=\sigma(\mathcal{R}^{0,2})$, show that $\displaystyle A_0 \in \mathcal{B}^2$, where $\displaystyle \mathcal{R}^{0,2}$ is the collection of two-dimensional bounded rectangles of the form$\displaystyle B(a_1,b_1,a_2,b_2) = \{(x,y):a_1<x \leq b_1, a_2< y \leq b_2\}$ with $\displaystyle a_1,b_1,a_2,b_2 \in [0,1]$, and $\displaystyle a_1 \leq b_1, a_2 \leq b_2$